WebDAV and WebAPI together cause Error: Handler “ExtensionlessUrlHandler-Integrated-4.0” has a bad module “ManagedPipelineHandler” in its module list

There are two things to check that you have appropriate installed .Net. And also the following configurations are checked.

An extract from my web.config around the ExtensionlessUrlHandler-Integrated-4.0.

Looking at the difference between yours and mine I don't have this section resourceType="Unspecified" requireAccess="Execute". I also use verb="*" that shouldn't make a difference but might be worth a try.

Also note I do not have accessPolicy="Read, Execute, Script" attribute in the handlers section. I also do not remove WebDAV.

<system.webServer>
    <handlers>
        <remove name="ExtensionlessUrlHandler-Integrated-4.0" />
        <remove name="OPTIONSVerbHandler" />
        <remove name="TRACEVerbHandler" />
        <add name="ExtensionlessUrlHandler-Integrated-4.0" path="*." verb="*" type="System.Web.Handlers.TransferRequestHandler" preCondition="integratedMode,runtimeVersionv4.0" />
    </handlers>
</system.webServer>

Possible answer from: https://stackoverflow.com/a/18458139/1398425

<system.webServer>
  <httpProtocol>
    <customHeaders>
      <add name="Access-Control-Allow-Origin" value="*" />
      <add name="Access-Control-Allow-Methods" value="GET,PUT,POST,DELETE" />
      <add name="Access-Control-Allow-Headers" value="Content-Type" />
    </customHeaders>
  </httpProtocol>
  <modules runAllManagedModulesForAllRequests="false">
    <remove name="WebDAVModule" />
  </modules>

  <validation validateIntegratedModeConfiguration="false" />
  <handlers>
    <remove name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" />
    <remove name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" />
    <remove name="ExtensionlessUrlHandler-Integrated-4.0" />
    <add name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" modules="IsapiModule" scriptProcessor="%windir%\Microsoft.NET\Framework\v4.0.30319\aspnet_isapi.dll" preCondition="classicMode,runtimeVersionv4.0,bitness32" responseBufferLimit="0" />
    <add name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" modules="IsapiModule" scriptProcessor="%windir%\Microsoft.NET\Framework64\v4.0.30319\aspnet_isapi.dll" preCondition="classicMode,runtimeVersionv4.0,bitness64" responseBufferLimit="0" />
    <add name="ExtensionlessUrlHandler-Integrated-4.0" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE" type="System.Web.Handlers.TransferRequestHandler" preCondition="integratedMode,runtimeVersionv4.0" />
  </handlers>
</system.webServer>